What is Cube Root of 512

• Cube root of 512 is written as $\sqrt[3]{512}$ (Radical form).
• $\sqrt[3]{512}$ = $\sqrt[3]{8 \times 8 \times 8}$ = 8
• In the exponential form, the cube root of 512 is expressed as $(512)^\frac{1}{3}$.

Prime Factorization Method

• Step 1: Prime factors of 512: 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2
• Step 2: Prime factors of 512 in triplets: (2 x 2 x 2) x (2 x 2 x 2) x (2 x 2 x 2)
• Step 3: Now cube root of 512:

$\sqrt[3]{512} = \sqrt[3]{(2 \times 2 \times 2) \times (2 \times 2 \times 2) \times (2 \times 2 \times 2)}$

$\sqrt[3]{512} = \sqrt[3]{ 2^3 \times2^3 \times2^3}$

$\sqrt[3]{512} = \sqrt{(2\times2\times2)^3}$

$\sqrt[3]{512} = \sqrt{8^3}$

$\sqrt[3]{512} = 8$

Therefore, the cube root of 512 is 8